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3 years ago

Using the greatest common factor, reduce the fraction 32/48 to its simplest form.

Mathematics

2 answers:

Romashka-Z-Leto [24]3 years ago

6 0

16/24 = 4/6 = 2/3
Simplest form is A. 2/3

anygoal [31]3 years ago

5 0

Answer:

2/3

Step-by-step explanation:

16 is the greatest common factor

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3 years ago

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car

Artyom0805 [142]

Answer:

Therefore $98 is be charged a bus containing 30 people.

Step-by-step explanation:

Given that,

A state park charges an entrance fee based on the number of people in vehicle.

Let the entry fee for the vehicle be E and entry fee for each person be x.

Then

C= E+(P×x)

C= Total charge in $

E= entry fee for a vehicle

P=No. of person

x= Entry charge per person.

Given A car containing 2 people charged $14

C=$14, P=2

∴14= E+(2× x)

⇒E+2x=14.....(1)

Again A car containing 4 people charged $20

C=$20, P=4

∴20= E+(4× x)

⇒E+4x=20.....(2)

Subtract (1) from (2), we get

E+4x-(E+2x)= 20-14

⇒E+4x-E-2x=6

⇒2x=6

⇒x=3

Putting the value of x in equation (1)

E+(2×3)=14

⇒E=14-6

⇒E=8

Therefore E=$8 and x=$3

Next we check whether our assumption is correct or wrong. Putting the value of E and x for third case

Here P= 8

Therefore C= E+(P×x)

= 8+(8× 3)

=8+24

=$32

Therefore our assumption is correct.

Now C=? , P= 30

The charged for the 30 people is

C= $[8+(30×3)]

=$[8+90]

=$98

Therefore $98 is be charged a bus containing 30 people.

4 0

4 years ago

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

Naddika [18.5K]

Answer:

The rocket will hit the ground after about 8.20 seconds.

Step-by-step explanation:

The height of the rocket y, in feet, x seconds after launch is modeled by the equation:

$y=-16x^2+121x+83$

We want to find the time at which the rocket will hit the ground.

If it hits the ground, the height of the rocket y will be 0. Thus:

$0=-16x^2+121x+83$

We can solve for x. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = -16, b = 121, and c = 83. Substitute:

$\displaystyle x=\frac{-(121)\pm\sqrt{(121)^2-4(-16)(83)}}{2(-16)}$

Simplify:

$\displaystyle x=\frac{-121\pm\sqrt{19953}}{-32}$

Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:

$\displaystyle x=\frac{121\pm3\sqrt{2217}}{32}$

Therefore, our two solutions are:

$\displaystyle x=\frac{121+3\sqrt{2217}}{32}\approx 8.20\text{ or } x=\frac{121-3\sqrt{2217}}{32}\approx -0.63$

Since time cannot be negative, we can ignore the second solution.

Therefore, the rocket will hit the ground after about 8.20 seconds.

7 0

3 years ago